1. Purdue Aeroelasticity
AAE 556 Aeroelasticity
Lecture 15
Finite element subsonic aeroelastic models
I like algebra
Algebra is my friend.
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2. Lift computation idealizations
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3. Purdue Aeroelasticity
Everything you wanted to know about aerodynamics but were afraid to ask
Lift per unit length l(y) changes along the span of a 3-D wing
The 2-D lift curve slope is not the same as the 3-D lift curve slope
Lift curve slope in degrees
e = Oswald’s efficiency factor
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4. Purdue Aeroelasticity
Lift
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5. Aerodynamic strip theory
Wing is sub-divided into a set of small spanwise strips
The lift and pitching moment on each strip is modeled as if the strip had infinite span
There is no aerodynamic interaction
There is limited or no aerodynamic influence between elements
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6. Purdue Aeroelasticity
Paneling methods
The wing is replaced by a thin surface
This surface is replaced by a finite number of elements or panels with aerodynamic features such as singularities
There is an aerodynamic influence coefficient matrix with interactive elements
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7. Strip theory gives different results
Source: G. Dimitriadis, University of Liege
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8. Purdue Aeroelasticity
Background
Gray and Schenk
NACA TN-3030
1952
Adapted for composites 1978
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9. Paneling - idealization requirements and limitations
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10. Panel aero model finding the lift distribution
pi=rVGi
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11. Lifting line wing model
Horseshoe vortices with varying strength
bound at 1/4 chord points
Downwash matching points at 3/4 chord
trailing vortices extending to infinity
The wing can be unswept or have non-constant chord
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12. Purdue Aeroelasticity
Panel aerodynamics interacts because of downwash (angle of attack) matching
Each horseshoe vortex creates a flow field around it. The 3/4 chord downwash is affected by every other vortex on the wing. The vortex strengths must be adjusted so that all conditions are satisfied.
Vortex influence decays with distance
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13. Aerodynamic relationship
Solving for vortex strengths allow us to approximate the lift distribution
wing
Relationship between local angle of attack and segment lift values.
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14. Aero matrix equation development
Matrix is square, but not symmetrical
ai=arigid + qstructural + acontrol
Matrix elements are functions of wing planform geometry
2D lift curve slope
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15. Structural idealization
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16. Each panel has its own FBD and panel geometry
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17. Purdue Aeroelasticity
Put them all together to get the static equilibrium equations – this is where the aeroelastic interaction occurs
local angles
lift on each element
dynamic pressure
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18. Purdue Aeroelasticity
Wing Geometry
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19. Purdue Aeroelasticity
Flexible and Rigid lift distributions (M=0.5) areas under each curve are equal
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20. Flexible and Rigid lift distribution (M=0.6)
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21. Rigid and flexible roll effectiveness (pb/2V)
MRev= 0.55
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22. Rigid wing and flexible wing
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23. Divergence Mach number
Divergence Mach No. = 0.590
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24. Purdue Aeroelasticity
Summary
Use of bound vortices creates a math model that can predict subsonic high aspect ratio wing lift distribution.
This model has been incorporated into a MATLAB code that you will use to do some homework exercises to calculate divergence, lift effectiveness and control effectiveness.
You will compare the trends previously derived
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